Linear time recognition of P4-indifference graphs

A graph is a P4-indifference graph if it admits an ordering < on its vertices such that every chordless path with vertices a, b, c, d and edges ab, bc, cd has

Linear Time Recognition of P4-Indifferent Graphs

A simple graph is P4-indifferent if it admits a total order b > c > d. P4-indifferent graphs generalize indifferent graphs and are perfectly orderable. Recently, Hoang,Maray and Noy gave a characterization of P4-indifferent graphs interms of forbidden induced subgraphs. We clarify their proof and describe a linear time algorithm to recognize P4-indifferent graphs. Whenthe input is a P4-indifferent graph, then the algorithm computes an order < as above.Key words: P4-indifference, linear time, recognition, modular decomposition.

On the Recognition of Bipolarizable and P_4-simplicial Graphs

The classes of Raspail (also known as Bipolarizable) and P_4-simplicial graphs were introduced by Hoàng and Reed who showed that both classes are perfectly orderable and admit polynomial-time recognition algorithms HR1. In this paper, we consider the recognition problem on these classes of graphs and present algorithms that solve it in O(n m) time. In particular, we prove properties and show that we can produce bipolarizable and P_4-simplicial orderings on the vertices of the input graph G, if such orderings exist, working only on P_3s that participate in a P_4 of G. The proposed recognition algorithms are simple, use simple data structures and both require O(n + m) space. Additionally, we show how our recognition algorithms can be augmented to provide certificates, whenever they decide that G is not bipolarizable or P_4-simplicial; the augmentation takes O(n + m) time and space. Finally, we include a diagram on class inclusions and the currently best recognition time complexities for a number of perfectly orderable classes of graphs

Linear time recognition of P4-indifference graphs

Theme 1 - Reseaux et systemes. Projet HYPERCOMSIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1999 n.3779 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Linear time recognition of P4-indifference graphs

A graph is a P4-indifference graph if it admits an ordering < on its vertices such that every chordless path with vertices a, b, c, d and edges ab, bc, cd has

Linear time recognition of P4-indifference graphs

A graph is a P4-indifference graph if it admits an ordering &lt; on its vertices such that every chordless path with vertices a, b, c, d and edges ab, bc, cd has a&lt;b&lt;c&lt;d or d&lt;c&lt;b&lt;a. We present a linear time recognition for these graphs

Linear time recognition of P4-indifference graphs

This paper shows how a linear time algorithm for the P 4 -indifference graphs recognition can be designed. This algorithm strongly relies on modular decomposition as a preprocessing. But linear time modular decomposition algorithms are still complicated to program. So the natural question is: can this preprocessing step be avoided ? So it has been shown that prime P 4 -indifference graphs are interval graphs. It is well known that Lexicographic Breadth First Search (Lex-BFS) [RTL76] plays an important role on interval graphs [HM91, COS98, HMPV97]. The order Lex-BFS visits the vertices of the input graph can be seen as the output of Lex-BFS: a Lex-BFS ordering. For example in [COS98], 4 sweeps of particular Lex-BFS are used to compute a characteristic ordering of interval graphs (the i-th sweep starts on the last visited vertex of the previous sweep). One can wonder if Lex-BFS can be used to compute a P 4 -indifference ordering. As illustrated by the graph of figure 4, the answer is n